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Garrett, Lauretta – Journal of Developmental Education, 2013
Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…
Descriptors: Adult Education, Adult Learning, Developmental Programs, Mathematics Education
Liu, Jun; Sha, Sha; Zheng, Qinghua; Zhang, Wei – International Journal of Distance Education Technologies, 2012
Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…
Descriptors: Foreign Countries, Knowledge Level, Difficulty Level, Educational Technology
Psycharis, Giorgos; Latsi, Maria; Kynigos, Chronis – International Journal for Technology in Mathematics Education, 2009
This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…
Descriptors: Elementary School Mathematics, Mathematics Instruction, Mathematical Concepts, Mathematics Activities
Arzarello, Ferdinando – 2000
This paper focuses on some cognitive and didactical phenomena that feature processes and products of pupils in grades 7-12 who learned mathematical proof within technological environments. The main issues in the analysis of students' performances consist of metaphors, deictics, mental times, narratives, functions of dragging, abductions, and…
Descriptors: Cognitive Structures, Elementary Secondary Education, Knowledge Representation, Learning Strategies
Alexander, Nancy – 1997
This paper reports on a study of seventh grade students (N=4) who attend a rural K-12 school. Students participated in a 5-week teaching experiment designed to build on their existing knowledge of the unit concept and extend it to the rational number operations of multiplication and division. Data collected comes in the form of videotapes,…
Descriptors: Arithmetic, Concept Formation, Division, Grade 7
Porzio, Donald T. – 1997
This research focuses on the graphics calculator in calculus and its impact on students' abilities to work with graphical, numerical, and symbolic representations. Three courses are compared, two of which are taught with less emphasis on the use of graphing calculators. The format of the course emphasizing calculator use is more traditional than…
Descriptors: Calculators, Calculus, Concept Formation, Educational Strategies
Smith, Frank – 2002
This book explores what makes mathematics possible as well as what makes mathematics difficult. Included is a discussion of the definition of mathematics, mathematics in language, the meaning of numbers, calculating and measuring, notation, numbers in space, and the best ways to learn mathematics. Historical information and practical examples are…
Descriptors: Cognitive Psychology, Cognitive Structures, Elementary Secondary Education, Higher Education
Bishop, Joyce Wolfer – 1997
This study explores seventh- and eighth-grade students' thinking about mathematical patterns. Interviews were conducted in which students solved problems about sequential perimeter and area problems modeled with pattern blocks and tiles, generalized the relationships related to the patterns and represented the relationships symbolically,…
Descriptors: Algebra, Concept Formation, Educational Strategies, Junior High Schools
Bolte, Linda A. – 1997
This study explores the combined use of concept maps and interpretive essays as a method of assessment in three mathematics courses. The primary objectives were to describe and document: (1) the use of concept maps and written essays to assess the connectedness of students' knowledge; (2) the correlation between students' scores on the concept…
Descriptors: Concept Formation, Concept Mapping, Elementary Secondary Education, Knowledge Level